Stylized Flames

[Albacore]

The best way to do this "J" is to manually trace the object. Use the padlock in the Layers palette so the your bit map doesn't move - Create a new layer and trace your shape from your locked bitmap. - Just use the Shape Editor Tool and very roughly go round your bitmap, not a great need to be all that accurate at this point. Take off any fill colour and give it a line thickness. - Now go round your shape editing, most of your shape has rounded corners so keep pressing "S" when you're on the control nodes to smooth, When editing your node handle try and keep the handles inline/parallel with the line it is trying to control.
Sorry I only spent under 10 mins doing your shape it will need better editing